The analytic bootstrap equations of non-diagonal two-dimensional CFT

Migliaccio, Santiago; Ribault, Sylvain

doi:10.1007/jhep05(2018)169

Cited by 28 publications

(109 citation statements)

References 7 publications

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“…The spectrum S 2Z,Z+ 1 2 was originally introduced as a guess that led to crossing-symmetric four-point functions, based on a numerical bootstrap analysis [9]. We now know that S 2Z,Z+ 1 2 is the non-diagonal sector of the odd CFT: an exactly solvable CFT that can be viewed as a limit of D-series minimal models [13].…”

Section: Progress In Understanding the Cftmentioning

confidence: 99%

“…If there exists a consistent CFT whose spectrum is S Potts , that CFT will certainly be much harder to solve than the odd CFT. The solution of the odd CFT relies on the existence of two independent degenerate fields, and this is reflected in the structure of the spectrum S 2Z,Z+ 1 2 , whose states are labelled by two integers [13]. On the other hand, states in S Potts are labelled by one integer and one fraction, so we expect that only one degenerate field exists.…”

Section: A Long Road To Solving the Potts Modelmentioning

confidence: 99%

“…The odd CFT actually exists for all central charges such that ℜc < 13 i.e. ℜβ 2 > 0 [9,13], and this more than covers the whole complex Q-plane via the map (1.2). The map is not one-to-one, and in particular each value of Q ∈ (4, ∞) corresponds to two complex conjugate values of c, giving rise to the phenomenon of walking renormalization group flows [10].…”

Section: General Complex Values Of Qmentioning

confidence: 99%

“…with the same left and right dimensions: these two fields however differ by their OPEs with other fields [13]. In order to describe cluster connectivities, we only need correlation functions of the fields V D P (0, 1 2 ) and V N (0, 1 2 ) .…”

mentioning

confidence: 99%

“…Assembling formulas for two-and three-point structure constants [13], we find the explicit expression of the four-point structure constants…”

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confidence: 99%

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On four-point connectivities in the critical 2d Potts model

Ribault²,

2019

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We perform Monte-Carlo computations of four-point cluster connectivities in the critical 2d Potts model, for numbers of states Q ∈ (0, 4) that are not necessarily integer. We compare these connectivities to four-point functions in a CFT that interpolates between D-series minimal models. We find that 3 combinations of the 4 independent connectivities agree with CFT four-point functions, down to the 2 to 4 significant digits of our Monte-Carlo computations. However, we argue that the agreement is exact only in the special cases Q = 0, 3, 4. We conjecture that the Potts model can be analytically continued to a double cover of the half-plane {ℜc < 13}, where c is the central charge of the Virasoro symmetry algebra.

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Section: Progress In Understanding the Cftmentioning

confidence: 99%

Section: A Long Road To Solving the Potts Modelmentioning

confidence: 99%

Section: General Complex Values Of Qmentioning

confidence: 99%

mentioning

confidence: 99%

“…Assembling formulas for two-and three-point structure constants [13], we find the explicit expression of the four-point structure constants…”

mentioning

confidence: 99%

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On four-point connectivities in the critical 2d Potts model

Ribault²,

2019

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Bootstrap approach to geometrical four-point functions in the two-dimensional critical Q-state Potts model: a study of the s-channel spectra

Jacobsen

Saleur

2019

J. High Energ. Phys.

160

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We revisit in this paper the problem of connectivity correlations in the Fortuin-Kasteleyn cluster representation of the two-dimensional Q-state Potts model conformal field theory. In a recent work [1], results for the four-point functions were obtained, based on the bootstrap approach, combined with simple conjectures for the spectra in the different fusion channels. In this paper, we test these conjectures using lattice algebraic considerations combined with extensive numerical studies of correlations on infinite cylinders. We find that the spectra in the scaling limit are much richer than those proposed in [1]: they involve in particular fields with conformal weight hr,s where r is dense on the real axis.

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Geometrical four-point functions in the two-dimensional critical Q-state Potts model: connections with the RSOS models

Grans-Samuelsson

Jacobsen

et al. 2020

J. High Energ. Phys.

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The "bootstrap determination" of the geometrical correlation functions in the two-dimensional Potts model proposed in a paper by Picco et al. [1] was later shown in [2] to be incorrect, the actual spectrum of the model being considerably more complex than initially conjectured. We provide in this paper a geometrical interpretation of the fourpoint functions built in [1], and explain why the results obtained by these authors, albeit incorrect, appeared so close to those of their numerical simulations of the Potts model. Our strategy is based on a cluster expansion of correlation functions in RSOS minimal models, and a subsequent numerical and algebraic analysis of the corresponding s-channel spectrum, in full analogy with our early work on the Potts model [2]. Remarkable properties of the lattice amplitudes are uncovered, which explain in particular the truncation of the spectrum of [2] to the much simpler one of the RSOS models, and which will be used in a forthcoming paper to finally determine the geometrical four-point functions of the Potts model itself.

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The analytic bootstrap equations of non-diagonal two-dimensional CFT

Cited by 28 publications

References 7 publications

On four-point connectivities in the critical 2d Potts model

On four-point connectivities in the critical 2d Potts model

Bootstrap approach to geometrical four-point functions in the two-dimensional critical Q-state Potts model: a study of the s-channel spectra

Geometrical four-point functions in the two-dimensional critical Q-state Potts model: connections with the RSOS models

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